That legislation upholds work permits for certain immigrant children and allows them to stay in the U.S. without deportation concerns. It could also reverse Obama's executive order that keeps immediate family members of U.S. citizens and permanent residents from being deported, The Hill noted.

At least three GOP senators have noted their concerns, fearing a hold-up could shut down the Homeland Security agency itself. They included Illinois' Mark Kirk, Maine's Susan Collins and Nevada's Dean Heller, The Hill said.

Democrats are moving quickly to cut down Republican opposition blocking Obama's executive order, which impacts about 5 million immigrants, Bloomberg noted of the expected fight.

After Tuesday's vote, the ball goes back to the House where Speaker John Boehner must decide whether to hold it up or move ahead.

Noted Bloomberg: "Republicans are trying to use a spending bill for the Department of Homeland Security to force the president to abandon the immigration orders he announced in November."

Such strategy seems doomed at the outset. Obama has pledged to veto the spending bill and it is unlikely, Bloomberg said, that Republicans will get the needed 60 Senate votes to move their plan ahead. The current Homeland spending bill runs out Feb. 27.